Abstract: Proofs of two results about a monomial ideal - describing membership in auxiliary ideals associated to the monomial ideal - are given which do not invoke resolution of singularities. The AM-GM inequality is used as a substitute for taking a log resolution of the monomial ideal.

Robert Lazarsfeld. Positivity in algebraic geometry. II, volume 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Positivity for vector bundles, and multiplier ideals. Springer-Verlag, Berlin, 2004. MR 2095472 (2005k:14001b)